Mithril protocol simulation

info

• This demo will improve your understanding of the Mithril protocol. By engaging with it, you will gain insights into how participants interact to create a multi-signature and understand the impact of the protocol parameters.

• This simulation is run by a CLI that you will build and run, and that will ultimately generate real Mithril multi-signatures.

• For reproducibility of the results, the simulation uses a deterministic source of randomness.

• During the simulation, some artifacts will be written to an artifacts folder, such as verification keys, individual signatures and multi signatures.

Prerequisites

Ensure you have the following:

• A computer running Linux (preferred) or macOS
• The latest stable version of the correctly configured Rust toolchain.

Download the source

You can download the source file from GitHub (HTTPS):

git clone https://github.com/input-output-hk/mithril.git

Or (SSH):

git clone git@github.com:input-output-hk/mithril.git

Build the Mithril protocol demo binary

Change the directory:

cd mithril/demo/protocol-demo

Run tests (optional):

make test

Build the executable:

make build

Verify the build

Check that the Mithril client binary is working correctly by running its help function:

./mithrildemo -h

You should see:

mithrildemo 
Simple demonstration of the Mithril protocol

USAGE:
    mithrildemo [OPTIONS]

OPTIONS:
    -h, --help                     Print help information
    -k, --k <K>                    Quorum parameter [default: 5]
    -m, --m <M>                    Security parameter, upper bound on indices [default: 200]
        --nmessages <NMESSAGES>    Number of messages to sign [default: 1]
        --nparties <NPARTIES>      Number of parties [default: 5]
        --phi-f <PHI_F>            f in phi(w) = 1 - (1 - f)^w, where w is the stake of a
                                   participant [default: 0.2]

Run the simulation

tip

A friendly reminder about the protocol parameters:

• k: the quorum parameter represents the minimum number of individual signatures (gathered from multiple participants) required to be aggregated in a multi-signature.
• m: the security parameter represents the total number of lotteries in which each participant can participate to sign the message.
• phi-f: the parameter that controls the probability of a participant winning a lottery. It varies between 0.0 (less chance) and 1.0 (more chance).

danger

The security level of the protocol is highly dependent on the value of the protocol parameters.

Therefore, these protocol parameters will be carefully selected by Mithril cryptographers and researchers to guarantee that only genuine stakeholders representing a sufficient threshold of the total stake can combine their individual signatures in a valid multi-signature.

Case 1: produce a multi-signature

Run the simulation with 5 participants:

./mithrildemo -k 5 -m 50 --phi-f 0.65 --nparties 5

The simulation should succeed and produce (or aggregate) a multi-signature:

>> Launch Mithril protocol demonstrator with configuration: 
Config {
    m: 50,
    k: 5,
    phi_f: 0.65,
    nparties: 5,
    nmessages: 1,
}

>> Protocol establishment phase
Party #0: party created with 826 stakes
Party #1: party created with 741 stakes
Party #2: party created with 144 stakes
Party #3: party created with 734 stakes
Party #4: party created with 41 stakes
Protocol established to StmParameters { m: 50, k: 5, phi_f: 0.65 }

>> Protocol initialization phase:
Verifier: verifier created
Verifier: protocol params updated to StmParameters { m: 50, k: 5, phi_f: 0.65 }
Party #0: protocol params updated to StmParameters { m: 50, k: 5, phi_f: 0.65 }
Party #1: protocol params updated to StmParameters { m: 50, k: 5, phi_f: 0.65 }
Party #2: protocol params updated to StmParameters { m: 50, k: 5, phi_f: 0.65 }
Party #3: protocol params updated to StmParameters { m: 50, k: 5, phi_f: 0.65 }
Party #4: protocol params updated to StmParameters { m: 50, k: 5, phi_f: 0.65 }
Verifier: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #0: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #1: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #2: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #3: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #4: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Artifacts written to artifacts/parties-keys.json

>> Protocol operations phase:
Message #0 to sign: [119, 36, 224, 63, 184, 216, 74, 55, 106, 67, 184, 244, 21, 24, 161, 28]
Party #0: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #0: lottery #2 won
Party #0: lottery #3 won
Party #0: lottery #8 won
Party #0: lottery #13 won
Party #0: lottery #16 won
Party #0: lottery #17 won
Party #0: lottery #19 won
Party #0: lottery #23 won
Party #0: lottery #25 won
Party #0: lottery #28 won
Party #0: lottery #29 won
Party #0: lottery #31 won
Party #0: lottery #42 won
Party #0: lottery #43 won
Party #0: lottery #46 won
Party #1: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #1: lottery #2 won
Party #1: lottery #3 won
Party #1: lottery #8 won
Party #1: lottery #13 won
Party #1: lottery #16 won
Party #1: lottery #17 won
Party #1: lottery #19 won
Party #1: lottery #23 won
Party #1: lottery #25 won
Party #1: lottery #29 won
Party #1: lottery #31 won
Party #1: lottery #42 won
Party #1: lottery #43 won
Party #1: lottery #46 won
Party #2: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #2: lottery #19 won
Party #2: lottery #43 won
Party #2: lottery #46 won
Party #3: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #3: lottery #2 won
Party #3: lottery #3 won
Party #3: lottery #8 won
Party #3: lottery #13 won
Party #3: lottery #16 won
Party #3: lottery #17 won
Party #3: lottery #19 won
Party #3: lottery #23 won
Party #3: lottery #25 won
Party #3: lottery #29 won
Party #3: lottery #31 won
Party #3: lottery #42 won
Party #3: lottery #43 won
Party #3: lottery #46 won
Party #4: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #4: lottery #19 won
Party #0: aggregate signature computed
Party #1: aggregate signature computed
Party #2: aggregate signature computed
Party #3: aggregate signature computed
Party #4: aggregate signature computed
Artifacts written to artifacts/single-signatures.json
Artifacts written to artifacts/multi-signatures.json

>> Protocol certificate verification phase:
Message #0 to verify: 7724e03fb8d84a376a43b8f41518a11c
Party #0: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Verifier: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Party #1: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Verifier: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Party #2: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Verifier: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Party #3: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Verifier: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Party #4: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!
Verifier: aggregate signature successfully verified for 7724e03fb8d84a376a43b8f41518a11c!

>> Congratulations, the protocol terminated with success.

Case 2: does not produce a multi-signature

Run the simulation with 5 participants:

./mithrildemo -k 5 -m 5 --phi-f 0.25 --nparties 5

The simulation should fail and not produce (or aggregate) any multi-signature:

>> Launch Mithril protocol demonstrator with configuration: 
Config {
    m: 5,
    k: 5,
    phi_f: 0.25,
    nparties: 5,
    nmessages: 1,
}

>> Protocol establishment phase:
Party #0: party created with 826 stakes
Party #1: party created with 741 stakes
Party #2: party created with 144 stakes
Party #3: party created with 734 stakes
Party #4: party created with 41 stakes
Protocol established to StmParameters { m: 5, k: 5, phi_f: 0.25 }

>> Protocol initialization phase:
Verifier: verifier created
Verifier: protocol params updated to StmParameters { m: 5, k: 5, phi_f: 0.25 }
Party #0: protocol params updated to StmParameters { m: 5, k: 5, phi_f: 0.25 }
Party #1: protocol params updated to StmParameters { m: 5, k: 5, phi_f: 0.25 }
Party #2: protocol params updated to StmParameters { m: 5, k: 5, phi_f: 0.25 }
Party #3: protocol params updated to StmParameters { m: 5, k: 5, phi_f: 0.25 }
Party #4: protocol params updated to StmParameters { m: 5, k: 5, phi_f: 0.25 }
Verifier: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #0: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #1: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #2: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #3: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Party #4: protocol keys registration from [("0", 826), ("1", 741), ("2", 144), ("3", 734), ("4", 41)]
Artifacts written to artifacts/parties-keys.json

>> Protocol operations phase:
Message #0 to sign: [119, 36, 224, 63, 184, 216, 74, 55, 106, 67, 184, 244, 21, 24, 161, 28]
Party #0: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #1: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #2: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #3: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #4: sign message 7724e03fb8d84a376a43b8f41518a11c
Party #0: not enough signatures to compute aggregate
Party #1: not enough signatures to compute aggregate
Party #2: not enough signatures to compute aggregate
Party #3: not enough signatures to compute aggregate
Party #4: not enough signatures to compute aggregate
Artifacts written to artifacts/single-signatures.json
Artifacts written to artifacts/multi-signatures.json

>> Protocol certificate verification phase:
Message #0 to verify: 7724e03fb8d84a376a43b8f41518a11c
Party #0: aggregate signature not found 7724e03fb8d84a376a43b8f41518a11c

>> Certificate verification failed: aggregate signature not found.

tip

For more information about the Mithril protocol, refer to the about Mithril section.